Problem: What do the following two equations represent? $5x+y = 2$ $20x+4y = -2$
Solution: Putting the first equation in $y = mx + b$ form gives: $5x+y = 2$ $y = -5x+2$ Putting the second equation in $y = mx + b$ form gives: $20x+4y = -2$ $4y = -20x-2$ $y = -5x - \dfrac{1}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.